The paper deals with the sampled-data implementation of controllers designed by means of Immersion and Invariance stabilization techniques for a special class of dynamics. A multi-rate digital control law is derived to preserve at the sampling instants manifold attractivity. The immersion condition is guaranteed under sampling and invariance on the manifold is recovered asymptotically by the multi-rate controller, particularly well suited for the class of systems considered. The effectiveness of the proposed digital solution is shown through numerical simulations of an academic example.